References
- Irving JH, Kirkwood JG. The statistical mechanics theory of transport processes IV the equations of hydrodynamics. J Chem Phys. 1950;18:817–829.
- Parker EN. Tensor virial equations. Phys Rev. 1954;96:1686–1689.
- Evans DJ, Morriss GP. Statistical mechanics of non-equilibrium liquids. 2nd ed. Canberra: Australian National University Press; 2007.
- Hardy RJ. Formulas for determining local properties in molecular dynamics simulations: shock waves. J Chem Phys. 1982;76:622–628.
- Murdoch AI. A critique of atomistic definitions of the stress tensor. J Elasticity. 2007;88:113–140.
- Murdoch AI. On molecular modelling and continuum concepts. J Elasticity. 2010;100:33.
- Admal NC, Tadmor EB. A unified interpretation of stress in molecular systems. J Elasticity. 2010;100:63–143.
- Cormier J, Rickman JM, Delph TJ. Stress calculation in atomistic simulations of perfect and imperfect solids. J Appl Phys. 2001;89:99–104.
- Lutsko JF. Stress and elastic constants in anisotropic solids: molecular dynamics techniques. J Appl Phys. 1988;64:1152–1154.
- Todd BD, Daivis PJ. Nonequilibrium molecular dynamics: theory, algorithms and applications. Cambridge (UK): Cambridge University Press; 2017.
- Todd BD, Evans DJ, Daivis PJ. Pressure tensor for inhomogeneous fluids. Phys Rev E. 1995;52:1627–1638.
- Han M, Lee JS. Method for calculating the heat and momentum fluxes of inhomogeneous fluids. Phys Rev E. 2004;70:061205.
- Heyes DM, Smith ER, Dini D, et al. The equivalence between volume averaging and method of planes definitions of the pressure tensor at a plane. J Chem Phys. 2011;135:024512.
- Varnik F, Baschnagel J, Binder K. Molecular dynamics results on the pressure tensor of polymer films. J Chem Phys. 2000;113(10):4444–4453. DOI:https://doi.org/10.1063/1.1288390.
- Walton J, Tildesley D, Rowlinson J, et al. The pressure tensor at the planar surface of a liquid. Mol Phys Mol Phys. 1983;48:1357–1368. DOI:https://doi.org/10.1080/00268978300100971.
- Harasima A. Molecular theory of surface tension. Adv Chem Phys. 1958;1:203–237.
- Rowlinson JS, Widom B. Molecular theory of capillarity (Dover books on chemistry). New York: Dover Publications; 2002.
- Schofield P, Henderson JR. Statistical mechanics of inhomogeneous fluids. Proc R Soc Lond A. 1982;379:231–246.
- Shi K, Santiso EE, Gubbins KE. Can we define a unique microscopic pressure in inhomogeneous fluids? J Chem Phys. 2021;154(8):084502. DOI:https://doi.org/10.1063/5.0044487.
- van Dijk D. Comment on ‘Pressure enhancement in carbon nanopores: a major confinement effect’ Long Y, Palmer JC, Coasne B, Liwinska-bartkowiak M and Gubbins KE, Phys Chem Chem Phys. 2011;13:17163. Phys Chem Chem Phys. 2020;22:9824–9825.
- Long Y, Palmer JC, Coasne B, et al. Reply to the ‘comment on Pressure enhancement in carbon nanopores: a major confinement effect’ van dijk D, Phys Chem Chem Phys. 2020;22. DOI: https://doi.org/10.1039/c9cp02890k. Phys Chem Chem Phys. 2020;22:9826–9830.
- Liu Y, Ganti R, Burton HGA, et al. Microscopic Marangoni flows cannot be predicted on the basis of pressure gradients. Phys Rev Lett. 2017;119:224502. DOI:https://doi.org/10.1103/PhysRevLett.119.224502.
- Malijevský A, Jackson G. A perspective on the interfacial properties of nanoscopic liquid drops. J Phys Condens Matter. 2012;24(46):464121.
- Zhou M. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proc R Soc Lond. 2003;459:2347–2392.
- Walton JPRB, Gubbins KE. The pressure tensor in an inhomogeneous fluid of nonspherical molecules. Mol Phys Mol Phys. 1985;55(3):679–688. DOI:https://doi.org/10.1080/00268978500101631.
- Hafskjold B, Ikeshoji T. Microscopic pressure tensor for hard-sphere fluids. Phys Rev E. 2002;66:011203. DOI: https://doi.org/10.1103/PhysRevE.66.011203.
- Shi K, Shen Y, Santiso EE, et al. Microscopic pressure tensor in cylindrical geometry: pressure of water in a carbon nanotube. J Chem Theory Comput. 2020;16(9):5548–5561. DOI: https://doi.org/10.1021/acs.jctc.0c00607.
- Chacón E, Tarazona P. Intrinsic profiles beyond the capillary wave theory: a Monte Carlo study. Phys Rev Lett. 2003;91(16):166103. DOI:https://doi.org/10.1103/PhysRevLett.91.166103.
- Pártay LB, Hantal G, Jedlovszky P, et al. A new method for determining the interfacial molecules and characterizing the surface roughness in computer simulations. application to the liquid–vapor interface of water. J Comput Chem. 2008;29(6):945–956. DOI:https://doi.org/10.1002/jcc.20852.
- Willard AP, Chandler D. Instantaneous liquid interfaces. J Phys Chem B. 2010;114(5):1954–1958. DOI:https://doi.org/10.1021/jp909219k.
- Jorge M, Jedlovszky P, Cordeiro MNDS. A critical assessment of methods for the intrinsic analysis of liquid interfaces. 1. Surface site distributions. J Phys Chem C. 2010;114(25):11169–11179. DOI:https://doi.org/10.1021/jp101035r.
- Sega M, Kantorovich SS, Jedlovszky P, et al. The generalized identification of truly interfacial molecules (itim) algorithm for nonplanar interfaces. J Chem Phys. 2013;138(4):044110. DOI:https://doi.org/10.1063/1.4776196.
- Braga C, Smith ER, Nold A, et al. The pressure tensor across a liquid-vapour interface. J Chem Phys. 2018;149(4):044705. DOI: https://doi.org/10.1063/1.5020991.
- Smith ER, Braga C. Hydrodynamics across a fluctuating interface. J Chem Phys. 2020;153(13):134705. DOI:https://doi.org/10.1063/5.0022530.
- Sega M, Fbin B, Jedlovszky P. Pressure profile calculation with mesh Ewald methods. J Chem Theory Comput. 2016;12(9):4509–4515. DOI:https://doi.org/10.1021/acs.jctc.6b00576.
- Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys. 1995;117(1):1–19. DOI:https://doi.org/10.1006/jcph.1995.1039.
- Tsai DH. The virial theorem and stress calculation in molecular dynamics. J Chem Phys. 1978;70:1375–1382.
- Smith ER, Heyes DM, Dini D, et al. Control-volume representation of molecular dynamics. Phys Rev E. 2012;85:056705.
- Heyes DM, Smith ER, Dini D, et al. The method of planes pressure tensor for a spherical subvolume. J Chem Phys. 2014;140(5):054506.
- Smith ER, Mller EA, Craster RV, et al. A Langevin model for fluctuating contact angle behaviour parametrised using molecular dynamics. Soft Matter. 2016;12:9604–9615. DOI:https://doi.org/10.1039/C6SM01980C.
- Smith ER. On the coupling of molecular dynamics to continuum computational fluid dynamics [PhD thesis]. London: Imperial College London; 2014.
- Smith ER. A molecular dynamics simulation of the turbulent Couette minimal flow unit. Phys Fluids. 2015;27(11):115105.
- Smith E. Flowmol. March 2021. DOI:https://doi.org/10.5281/zenodo.4639547.
- Petravic J, Harrowell P. The boundary fluctuation theory of transport coefficients in the linear-response limit. J Chem Phys. 2006;124:014103.
- Ramsey SD, Potter K, Hansen C. Ray bilinear patch intersections. J Graphics Tools. 2004;9(3):41–47. DOI:https://doi.org/10.1080/10867651.2004.10504896.
- Kirkwood JG, Buff FP. The statistical mechanical theory of surface tension. J Chem Phys. 1949;17(3):338–343.
- Sega M, Fbin B, Jedlovszky P. Layer-by-layer and intrinsic analysis of molecular and thermodynamic properties across soft interfaces. J Chem Phys. 2015;143(11):114709. DOI:https://doi.org/10.1063/1.4931180.